Definition:Diameter of Hyperbola
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This page is about Diameter of Hyperbola. For other uses, see Diameter.
Definition
Let $\KK$ be a hyperbola.
A diameter of $\KK$ is the locus of the midpoints of a system of parallel chords of $\KK$.
Also defined as
Some sources define the diameter of a hyperbola $\KK$ as a chord of $\KK$ which passes through the center of $\KK$:
However, while it is true that such a chord is indeed a diameter of $\KK$, not all diameter of $\KK$ are chords of $\KK$.
For example:
where it can be seen that the diameter (red) of the hyperbola (blue) defined by the parallel chords is not actually itself a chord of $\KK$.
Also see
- Results about diameters of conic sections can be found here.